If someone sells 271 bags of popcorn and made 447 dollars, with a large bag costing 3 dollars and a small one costing 1 dollar. How many bags did they sell?

Let x be big bag, y be small bag

X+y = 272

3x+y=447

Solve for y use substitution or subtraction which ever is best for you.

In my case I use subtraction, solve for y.

Subtract y on both equation.

You will get - 2x = - 175, x = 87.5. Plug in 87.5 solve for y. 184.5

Number of small bags = x

Number of large bags = y

x + 3y = 447

x + y = 271

Subtract the second equation from the first to get

2y = 176

y = 88

x = 183

I'm assuming you meant to say 'How many small/large bags did they sell?'

So ...

183 small bags and 88 large bags